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Question

Credit Card Debt John has a balance of $3000 on his Discover card that charges 1% interest per month on any unpaid balance. John can afford to pay$100 toward the balance each month. His balance each month after making a 100paymentisgivenbytherecursivelydefinedsequence100 payment is given by the recursively defined sequenceB_{0}=$3000 \quad B_{n}=1.01 B_{n-1}-100$ Determine John's balance after making the first payment. That is, determine B1B_{1}.

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We need to determine the first payment term (B1) for the following expression.\text{\color{#4257b2}We need to determine the first payment term\ $(B_{1})$\ for the following expression.}

B0=3000 Dollars            Bn=1.01 Bn1100\color{Brown}B_{0}=3000\text{\ Dollars}\ \ \ \ \ \ \ \ \ \ \ \ B_{n}=1.01\ B_{n-1}-100

\lozenge\ Solution:\text{\underline{\bf{Solution:}}}

To get any term, substitute the number of term in the expression which given as follows:

Bn=1.01 Bn1100B_{n}=1.01\ B_{n-1}-100

B0=3000B_{0}=3000

B1=1.01 B11100                    B1=1.01 B0100B_{1}=1.01\ B_{1-1}-100\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B_{1}=1.01\ B_{0}-100

B1=(1.013000)100                 B1=3030100B_{1}=(1.01\cdot3000)-100\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B_{1}=3030-100

B1=2930 DollarsB_{1}=2930\ \text{Dollars}

So, the first payment term is \ 29302930\ dollars

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